Gravitational wave detection using electromagnetic modes in a resonance cavity

We present a proposal for a gravitational wave detector, based on the excitation of an electromagnetic mode in a resonance cavity. The mode is excited due to the interaction between a large amplitude electromagnetic mode and a quasimonochromatic gravitational wave. The minimum metric perturbation needed for detection is estimated to the order 7 × 10 using current data on superconducting niobium cavities. Using this value together with different standard models predicting the occurrence of merging neutron star or black hole binaries, the corresponding detection rate is estimated to 1–20 events per year, with a ‘table top’ cavity of a few meters length. Submitted to: Class. Quantum Grav. PACS numbers: 04.80.Nn, 95.55.Ym, 95.85.Sz During the last decades the quest for detecting gravitational waves has intensified. The efforts have been inspired by the indirect evidence for gravitational radiation [1], advances in technology and the prospects of obtaining new useful astrophysical information through the development of gravitational wave astronomy [2]. A number of ambitious detector projects are already in operation or being built all over the world, for example Ligo and ALLEGRO in USA, Virgo, AURIGA and GEO 600 in Europe, Tama 300 in Japan, AIGO and NIOBE in Australia [3]. Furthermore, there are well developed plans to use space based gravitational wave detectors, i.e., the LISA project [4]. The detection mechanisms are basically of a mechanical nature in the cases above, but there have also been several proposals for electromagnetic detection mechanisms [5]. In the present paper we will investigate a detection mechanism based on the interaction of electromagnetic modes and gravitational radiation in a cavity with highly conducting walls. The main feature of our proposed gravitational wave detector is that it supports two electromagnetic eigenmodes with nearby eigenfrequencies, a possibility that has previously been discussed in Refs. [6, 7]. If one eigenmode is excited Letter to the Editor 2 initially (called the pump-mode), and a quasi-monochromatic gravitational wave with a frequency equal to the eigenmode frequency difference reaches our system, a new electromagnetic eigenmode can be excited due to the gravitational-electromagnetic wave interaction. The coupling mechanism is similar in principle to the wave interaction processes described in, e.g., Ref. [8]. The low-frequency nature of the gravitational modes, as compared to the electromagnetic resonance frequencies, at first seem to greatly limit the efficiency of a cavity with nearby frequencies. To get a large gravitationally induced mode-coupling for a simple cavity geometry, the estimated cavity dimensions become prohibitively large, i.e., comparable to the wavelength of the gravitational wave. Solutions to this problem has been found by Refs. [7], who has considered a gravitational wave detector consisting of two coupled cavities. Cavities based on these principles have been built, and experimental results are presented in Refs. [9]. In this letter we consider a single cavity with a variable crossection. The main purpose of varying the crossection is the following. For a cavity with dimensions much smaller than the wavelength of the gravitational wave, the suggested geometry greatly magnifies the gravitational wave induced mode-coupling. In our present work we have simulated the effect of a varying crossection, by considering a cavity filled with three different dielectrics, in order to be able to perform most of the calculations analytically. It is straightforward to make a semi-quantitative translation of our results to the case of a vacuum cavity with a varying crossection. Using current data on the latter type of cavity [10, 11, 12], we estimate the minimum detection level of the metric perturbation to the value hmin ≈ 7×10−23, where we have considered an inspiraling neutron star or black hole pair as a gravitational wave source. If such a level of sensitivity can be reached, neutron star or black hole binaries close to collapse could be detected at a distance rmax ∼ 10 ly. Adopting data from Ref. [13] for the occurrence of compact binary mergers, we obtain the estimate 1–20 detection events per year. In vacuum, a linearized gravitational wave can be represented by gμν = ημν+hμν(ξ) where ξ ≡ x− ct, and hxx = −hyy ≡ h+, hxy = hyx ≡ h× in standard notation. Neglecting terms proportional to derivatives of h+ and h×, the wave equation for the magnetic field is [14, 15] [ n c ∂ ∂t −∇ ] B = [ h+ ( ∂ ∂y − ∂ 2 ∂z ) + h× ∂